For a better understanding of the subsequent passages, the definitions of several terms frequently used in the following are provided.
Hamming Weight/Parity
The Hamming weight of a symbol composed of binary elements 0 and 1 (alternatively denoted −1 and 1) is the number of non-zero (i.e. 1) elements within a data word composed of binary elements. Consequently for any 4-bit word that is mapped onto a 16-QAM symbol the Hamming weight can be an integer value of 0 (i.e. for the word “0000”), of 1 (e.g. for the word “0010”), of 2 (e.g. for the word “1010”), of 3 (e.g. for the word “1110”), or of 4 (i.e. for the word “1111”). An even Hamming weight value is also denoted an “even Hamming parity”, an odd Hamming weight value is denoted an “odd Hamming parity”.
16-QAM
16-QAM (Quadrature Amplitude Modulation) is a digital modulation scheme which is commonly used—for example—in IMT 2000-based mobile communication systems, such as UMTS or CDMA 2000. The 16 modulation symbols are defined by distinct points in the complex signal space in which the 16-QAM constellation is commonly illustrated. Each of these points represents one 16-QAM symbol.
For binary information transmission systems, four different bits may be used to determine one of the existing 16-QAM symbols. Therefore one 16-QAM symbol consists (or can be represented by a data word) of 4 bits, and is represented by a complex value in the complex plane. Generally the complex value of a modulation symbol can be represented by its Cartesian inphase- and quadrature-components (I and Q components) relative to the respective I-axis and Q-axis in the complex plane. These axes also divide the complex plane in four quadrants. The representation of a modulation symbol by its real and imaginary part in the complex plane is equivalent to its representation by polar components, i.e. radius and angle.
In the following a data word that is mapped to a modulation symbol according to Gray 16 QAM will also be denoted by i1q1i2q2. This notation is intended to illustrate the mapping of the individual bits to inphase and quadrature component of the modulation symbol: i1 and i2 together form the inphase component of the symbol, while q1 and q2 together form the quadrature component thereof (or vice versa). Likewise, a data word that is mapped to a modulation symbol according to an AICO 16 QAM mapping (see below) will also be denoted by a1b1a2b2, where a1 and a2 together form the inphase component of the symbol, while b1 and b2 together form the quadrature component thereof (or vice versa).
It should be understood that both notations have been chosen for illustration purposes only and should not be understood as to limit the invention presented to a specific order of mapping the bits of a data word to inphase or quadrature component of a modulation symbol.
Gray Mapping or Gray Coding
Gray mapping or Gray coding are terms that are widely used in communication systems when digital modulation is used. Commonly, the so-called Gray mapping is used to associate the 16 modulation symbols in a 16-QAM constellation with a quadruple of bits which is mapped to the respective symbol. According to this Gray mapping scheme, adjacent modulation symbols in the horizontal or vertical direction differ in one bit only. An exemplary Gray 16-QAM constellation is illustrated in FIG. 21.
AICO mapping
In the copending international patent applications No. PCT/EP 2005/004891 and No. PCT/EP 2005/004892 a new definition of mapping rules of the 16-QAM constellation, a so-called AICO (Antipodal Inverted COnstellation) mapping, has been proposed. An exemplary 16-QAM symbol constellation according to this new proposed mapping scheme is illustrated in FIG. 22. As some embodiments of the invention will relate to this new mapping of modulation symbols, the key properties of AICO mapping will be briefly explained in the following.
FIG. 3 shows a mapping of even and odd Hamming weight words onto constellation symbols according to an AICO mapping scheme. In the constellation shown in FIG. 3, a special 16-QAM mapping fulfils at least the following properties:                All words that have a first Hamming weight parity (even/odd) are unambiguously mapped either onto the dashed or the white modulation symbols in FIG. 3.        All words that have a second Hamming weight parity (odd/even) are unambiguously mapped either onto the dashed or the white modulation symbols in FIG. 3.        The above two properties are complementary to each other, i.e. if the even Hamming weight words are mapped onto the dashed modulation symbols, then the odd Hamming weight words are mapped onto the white modulation symbols, or vice versa        Rotation of a first constellation symbol by 180 degrees results in a second constellation symbol that conveys a second word that is the binary complement of the first word that is conveyed by the first constellation symbol.        
FIG. 3 further illustrates a common denotation of distances within a square 16 QAM constellation, where modulation symbols closest to the axis of a complex coordinate plane have a Euclidian distance of d from the axis (resulting in an Euclidian distance of 2d=2√{square root over (D)} between nearest neighbor symbols).
As can be seen in FIG. 4, each dashed symbol in a 16-QAM constellation as in FIG. 3 has either two or four nearest neighbor symbols, and each white symbol in FIG. 3 has three nearest neighbor symbols. Therefore the first two properties above may be reformulated as follows:                All words that have a first Hamming weight parity are unambiguously mapped either onto modulation symbols with two nearest neighbors or with four nearest neighbors.        All words that have a second Hamming weight parity are unambiguously mapped onto modulation symbols with three nearest neighbors.        
A noteworthy consequence of these properties is that the Gray principle for closest neighboring symbols is violated in some cases. Therefore the proposed mapping may be denoted a non-Gray mapping.
The last property of the four properties defined above states that antipodal constellation symbols carry words that are binary inverted. Therefore this mapping is referred to as Antipodal Inverted Constellation Mapping. A consequence of the non-Gray characteristic is the difference of symbol regions which specific bits select.
As has been described in the two co-pending European applications mentioned above, AICO mapping may be advantageously employed for communications and allows for providing a modulation and coding scheme using a signal space expansion and 16-QAM which improves the bit-error rate in comparison to QPSK modulated signals. As far as mobile communication systems are concerned, AICO mapping further provides the possibility to implement coders and decoders with low complexity.
It is also desirable to have a simple mapping structure in a system that can be used to generate modulation symbols from bits according to the Gray mapping rules as well as according to the AICO mapping rules, without having to rely on a hardware implementation of both sets of mapping rules in parallel. This is mainly for complexity reasons, and also to allow an easy inclusion of the AICO mapping rules into legacy devices that support only the generation of modulation symbols according to Gray mapping rules. Likewise in new systems that support only the generation of modulation symbols according to AICO mapping rules, it may be desirable to be able to generate modulation symbols according to Gray mapping rules.
In the prior-art several approaches have been proposed to implement different mapping schemes.
For example, in US2003/72286A1 proposes a transmitting/receiving apparatus and method for packet retransmission in a mobile communication system. Upon request for a retransmission from a receiver, a transmitter inverts initially transmitted coded bits if the retransmission is odd-numbered for the same data, modulates the inverted bits, and transmits the modulated bits to the receiver. Then the receiver recovers the coded bits by demodulation. If the coded bits are retransmitted an odd number of times, the receiver decodes the coded bits after inversion. Thus the error probabilities of initial transmission bits and retransmission bits are averaged in effect and decoding performance is improved.
In WO 2004/036817A1, another application of the applicant, a method of transmitting data in a wireless communication system from a transmitter to a receiver comprising the steps of modulating data at the transmitter using a first signal constellation pattern to obtain a first data symbol. The first data symbol is transmitted to the receiver using a first diversity branch. Further, the data is modulated at the transmitter using a second signal constellation pattern to obtain a second data symbol. Then, the second data symbol is transmitted to the receiver over a second diversity branch. Finally, the received first and second data symbol are diversity combined at the receiver.
Though these prior-art examples show how different symbol mappings may be implemented using a single mapping unit working according to a given symbol mapping scheme, the use of these techniques to allow for providing both AICO mapping and Gray mapping will fail. In these prior-art techniques it is not possible to change the underlying Hamming distance structure of the mapping, i.e. to change the nearest-neighbor relations (Hamming distances) of the modulation symbols in the constellation.
Therefore it is not possible to generate an AICO mapping with a Gray symbol mapping unit (or vice versa) using the prior-art techniques, since the AICO mapping and Gray mapping scheme have different distributions with respect to the Hamming distance of data words representing nearest neighbors in a representation of the constellation of the modulation symbols of the modulation scheme.